I'm a man (adult human male) and am pretty invested in this topic - very much on the Gender Critical side of the debate.
I learned about the issues, initially from Mumsnet, and then from trying to read both sides in order to get a balanced view. What I found is that the only "balanced" view tends to be more on the GC side of the argument, whereas I think that most views and arguments on the side that would call itself "trans-inclusive" tend to be rather unbalanced, to put it mildly. So reading both sides brought me to a more intransigent set of views than where I started.
The closest version to a "balanced" narrative that I could find is to start by acknowledging that yes, there is very small group of genuinely gender dysphoric males who felt miserable in their bodies until they had surgery and started wearing clothes, etc. that make them look somewhat like biological females - and historically, their discreet presence in many otherwise female-only spaces was generally accepted and that was good for them.
However, there then came to be a much larger, louder, aggressive and well-funded movement of males, who furthermore hijacked several of the gay ray rights charities such as Stonewall, who want to bully everyone into pretending that males can become females, or that being female is subjective rather than objective and that sex is on a "spectrum" rather than binary. This movement of bullies demanded acceptance that men be permitted to invade and often dominate all of the previously sex-segregated female spaces where adult human females are most vulnerable to being dominated by them as males, including prisons, changing rooms, showers sleeping accommodation shared with strangers, and contact sports, etc.
This pissed me off. I do not like bullies. There are women whom I love and do not want to see subjected to bullying. So I became very invested in the topic, discussing it with friends both male and female, and supporting some of the organisations active on the GC side.
What I found is that most males with whom I have discussed this also lean very much towards the GC side. They just generally keep their mouths shut on this topic because they already get treated as automatic bigots for being male, white and over 50.
I also found that many people who describe themselves as "trans inclusive" would actually NOT agree that transwomen should be able to join in women's sports teams, get housed in women's prisons, etc.
There is still a small group of biological men who look enough like women that they are likely to be unsafe in men's single-sex spaces, and a dilemma remains around how to keep them safe, but solutions needs to be found that solve that without disadvantaging biological women.
That is what the recent SC ruling should lead to.